Crystal structures of alpha and beta modifications of Mn as packing of tetrahedral helices extracted from a four-dimensional {3, 3, 5} polytope

2020 ◽  
Vol 76 (5) ◽  
pp. 948-954
Author(s):  
Alexander Talis ◽  
Ayal Everstov ◽  
Valentin Kraposhin
Keyword(s):  
Crystal Structures ◽  
Twofold Axis ◽  
Structure Description ◽  
The Common

The crystal structures of both α- and β-Mn modifications have been presented as packing of tetrahedral helices extracted from four-dimensional {3, 3, 5} polytope construction. Presentation of the β-Mn structure as a primitive cubic arrangement formed by double tetrahedral helices around a central tetrahedral Coxeter–Boerdijk helix (tetrahelix) enables the inclusion in the structure description not only all atoms but also all tetrahedra; these tetrahedra are not accounted for in the preceding models for the β-Mn structure. The tetrahelix periodicity arising by minimal deformations of tetrahedra edges is equal to eight tetrahedra and coinciding with the lattice periods of both modifications. The linear substructure of α-Mn crystal consists of four tetrahelices which join to each other by edges around the common twofold axis. The α-Mn structure has been presented as primitive cubic arrangement constructed from such rods.

scholarly journals The Principle of Maximal Simplicity for Modular Inorganic Crystal Structures

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1472
Author(s):  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structures ◽  
Structure Prediction ◽  
Structural Information ◽  
Structural Complexity ◽  
Configurational Entropy ◽  
Sensu Stricto ◽  
Least Action ◽  
Inorganic Crystal ◽  
Principle Of Least Action ◽  
Structure Description

Modularity is an important construction principle of many inorganic crystal structures that has been used for the analysis of structural relations, classification, structure description and structure prediction. The principle of maximal simplicity for modular inorganic crystal structures can be formulated as follows: in a modular series of inorganic crystal structures, the most common and abundant in nature and experiments are those arrangements that possess maximal simplicity and minimal structural information. The latter can be quantitatively estimated using information-based structural complexity parameters. The principle is applied for the modular series based upon 0D (lovozerite family), 1D (biopyriboles) and 2D (spinelloids and kurchatovite family) modules. This principle is empirical and is valid for those cases only, where there are no factors that may lead to the destabilization of simplest structural arrangements. The physical basis of the principle is in the relations between structural complexity and configurational entropy sensu stricto (which should be distinguished from the entropy of mixing). It can also be seen as an analogy of the principle of least action in physics.

Crystal Structures of the Common Apolipoprotein E Variants: Insights into Functional Mechanisms

1993 ◽  
pp. 81-96 ◽  
Author(s):  
Mark R. Wardell ◽  
Charles Wilson ◽  
David A. Agard ◽  
Robert W. Mahley ◽  
Karl H. Weisgraber
Keyword(s):  
Apolipoprotein E ◽  
Crystal Structures ◽  
The Common ◽  
Functional Mechanisms

Trifluoromethyl Complexes of Osmium(II) by Halogen Oxidation of an Osmium(0) Difluorocarbene Compound and the Structures of Os(CF3)Cl2(NO)(PPh3)2 and Os(CF3)Cl0.666I1.333(NO)(PPh3)2

1986 ◽  
Vol 39 (9) ◽  
pp. 1315 ◽  
Author(s):  
GR Clark ◽  
TR Greene ◽  
WR Roper
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Crystal Structures ◽  
Octahedral Coordination ◽  
Space Group ◽  
Twofold Axis

Oxidation of Os(=CF2) Cl (NO)(PPh3)2 by the halogens X2(X = Cl , I), unexpectedly yields the trifluoromethyl complexes Os(CF3)CIX(NO)(PPh3)2 in a low yield which is improved by the addition of LiF to the reaction mixture. The crystal structures of both Os(CF3)Cl2(NO)(PPh3)2 and Os(CF3)Cl0.666I1.333(NO)(PPh3)2 have been determined. Crystals of Os(CF3)Cl2(NO)(PPh3)2 are monoclinic, a 24.543(5), b 9.685(1), c 15.951(1) Ǻ, β 115.81(1)°, Z 4, space group C2/c. Least-squares refinement has returned a residual, R, of 0.048 for 3371 observed reflections. The molecule lies on a twofold axis, with the CF3-group and one Cl-ligand statistically interchanged. Crystals of Os(CF3)Cl0.666 I1.333(NO)(PPh3)2 are monoclinic, a 24.562(4), b 9.690(1), c 16.385(2) Ǻ, β 115.51(1)°, Z 4, space group C2/c. Least-squares refinement has returned a residual of 0.058 for 4087 observed reflections. This crystal structure is best described as a 2 : 1 mixture of Os(CF3) ClI (NO)(PPh3)2 and s(CF3)I2(NO)(PPh3)2, (both with CF3 and I statistically disordered about the diad axis, as above). Both complexes exhibit octahedral coordination geometries.

scholarly journals Crystal structures and Hirshfeld surface analyses of bis[N,N-bis(2-methoxyethyl)dithiocarbamato-κ2S,S′]di-n-butyltin(IV) and [N-(2-methoxyethyl)-N-methyldithiocarbamato-κ2S,S′]triphenyltin(IV)

2018 ◽  
Vol 74 (3) ◽  
pp. 302-308 ◽  
Author(s):  
Rapidah Mohamad ◽  
Normah Awang ◽  
Nurul Farahana Kamaludin ◽  
Mukesh M. Jotani ◽  
Edward R. T. Tiekink
Keyword(s):  
Crystal Structures ◽  
Metal Atom ◽  
Three Dimensional ◽  
Hirshfeld Surface ◽  
Molecular Structures ◽  
Site Symmetry ◽  
Tetrahedral Geometry ◽  
Twofold Axis ◽  
Distorted Tetrahedral Geometry ◽  
Crystal And Molecular Structures

The crystal and molecular structures of the two title organotin dithiocarbamate compounds, [Sn(C4H9)2(C7H14NO2S2)2], (I), and [Sn(C6H5)3(C5H10NOS2)], (II), are described. Both structures feature asymmetrically bound dithiocarbamate ligands leading to a skew-trapezoidal bipyramidal geometry for the metal atom in (I) and a distorted tetrahedral geometry in (II). The complete molecule of (I) is generated by a crystallographic twofold axis (Sn site symmetry 2). In the crystal of (I), molecules self-assemble into a supramolecular array parallel to (10-1)viamethylene-C—H...O(methoxy) interactions. In the crystal of (II), supramolecular dimers are formedviapairs of weak phenyl-C—H...π(phenyl) contacts. In each of (I) and (II), the specified assemblies connect into a three-dimensional architecture without directional interactions between them. Hirshfeld surface analyses confirm the importance of H...H contacts in the molecular packing of each of (I) and (II), and in the case of (I), highlight the importance of short methoxy-H...H(butyl) contacts between layers.

scholarly journals Crystal structures of a series of bis(acetylacetonato)oxovanadium(IV) complexes containing N-donor pyridyl ligands

2020 ◽  
Vol 76 (6) ◽  
pp. 826-830
Author(s):  
Jeffrey A. Rood ◽  
Steven R. Reehl ◽  
Kaitlyn A. Jacoby ◽  
Allen Oliver
Keyword(s):  
Crystal Structures ◽  
The Other ◽  
Cryogenic Temperatures ◽  
Octahedral Structure ◽  
Twofold Axis ◽  
Pyridyl Ligands ◽  
Distorted Octahedral ◽  
Acta Crystallogr

Crystal structures for a series of bis(acetylacetonato)oxovanadium(IV) complexes containing N-donor pyridyl ligands are reported, namely, bis(acetylacetonato-κ2 O,O′)oxido(pyridine-κN)vanadium(IV), [V(C5H7O2)2O(C5H5N)], 1, bis(acetylacetonato-κ2 O,O′)oxido(pyridine-4-carbonitrile-κN)vanadium(IV), [V(C5H7O2)2O(C6H4N2)], 2, and bis(acetylacetonato-κ2 O,O′)(4-methoxypyridine-κN)oxidovanadium(IV), [V(C5H7O2)2O(C6H7NO)], 3, Compounds 1–3 have the formulae VO(C5H7O2)2 L, where L = pyridine (1), 4-cyano-pyridine (2), and 4-methoxypyridine (3). Compound 1 was previously reported [Meicheng et al. (1984). Kexue Tongbao, 29, 759–764 and DaSilva, Spiazzi, Bortolotto & Burrow (2007). Acta Crystallogr., E63, m2422] and redetermined here at cryogenic temperatures. Compounds 1 and 2 as pyridine and 4-cyanopyridine adducts, respectively, crystallize as distorted octahedral structures with the oxo and pyridyl ligands trans to one another. A crystallographic twofold axis runs through the O—V—N bonds. Compound 3 containing a 4-methoxypyridine ligand crystallizes as a distorted octahedral structure with the oxo and pyridyl ligands cis to one other, removing the twofold symmetry seen in the other complexes.

scholarly journals Crystal structures and Hirshfeld surface analysis of a series of 4-O-arylperfluoropyridines

2019 ◽  
Vol 75 (8) ◽  
pp. 1102-1107 ◽  
Author(s):  
Andrew J. Peloquin ◽  
Cynthia A. Corley ◽  
Sonya K. Adas ◽  
Gary J. Balaich ◽  
Scott T. Iacono
Keyword(s):  
Crystal Structures ◽  
Aromatic Ring ◽  
Dihedral Angle ◽  
Surface Analysis ◽  
Phenyl Ring ◽  
Pyridine Ring ◽  
Hirshfeld Surface ◽  
Hirshfeld Surface Analysis ◽  
Dihedral Angles ◽  
Twofold Axis

Five new crystal structures of perfluoropyridine substituted in the 4-position with phenoxy, 4-bromophenoxy, naphthalen-2-yloxy, 6-bromonaphthalen-2-yloxy, and 4,4′-biphenoxy are reported, viz. 2,3,5,6-tetrafluoro-4-phenoxypyridine, C11H5F4NO (I), 4-(4-bromophenoxy)-2,3,5,6-tetrafluoropyridine, C11H4BrF4NO (II), 2,3,5,6-tetrafluoro-4-[(naphthalen-2-yl)oxy]pyridine, C15H7F4NO (III), 4-[(6-bromonaphthalen-2-yl)oxy]-2,3,5,6-tetrafluoropyridine, C15H6BrF4NO (IV), and 2,2′-bis[(perfluoropyridin-4-yl)oxy]-1,1′-biphenyl, C22H8F8N2O2 (V). The dihedral angles between the aromatic ring systems in I–IV are 78.74 (8), 56.35 (8), 74.30 (7), and 64.34 (19)°, respectively. The complete molecule of V is generated by a crystallographic twofold axis: the dihedral angle between the pyridine ring and adjacent phenyl ring is 80.89 (5)° and the equivalent angle between the biphenyl rings is 27.30 (5)°. In each crystal, the packing is driven by C—H...F interactions, along with a variety of C—F...π, C—H...π, C—Br...N, C—H...N, and C—Br...π contacts. Hirshfeld surface analysis was conducted to aid in the visualization of these various influences on the packing.

True and brittle micas: composition and solid-solution series

2007 ◽  
Vol 71 (3) ◽  
pp. 285-320 ◽  
Author(s):  
G. Tischendorf ◽  
H.-J. Förster ◽  
B. Gottesmann ◽  
M. Rieder
Keyword(s):  
Solid Solution ◽  
Crystal Structures ◽  
Solid Solutions ◽  
Solid Solution Series ◽  
Octahedral Sheet ◽  
Tetrahedral Sheet ◽  
Solution Series ◽  
The Common ◽  
End Members ◽  
Graphical Presentation

AbstractMicas incorporate a wide variety of elements in their crystal structures. Elements occurring in significant concentrations in micas include: Si, IVAl, IVFe3+, B and Be in the tetrahedral sheet; Ti, VIAl, VIFe3+, Mn3+, Cr, V, Fe2+, Mn2+, Mg and Li in the octahedral sheet; K, Na, Rb, Cs, NH4, Ca and Ba in the interlayer; and O, OH, F, Cl and S as anions. Extensive substitutions within these groups of elements form compositionally varied micas as members of different solid-solution series. The most common true K micas (94% of almost 6750 mica analyses) belong to three dominant solid-solution series (phlogopite–annite, siderophyllite–polylithionite and muscovite–celadonite). Theirclassification parameters include: Mg/(Mg+Fetot) [=Mg#] formicas with VIR >2.5 a.p.f.u. and VIAl <0.5 a.p.f.u.; Fetot/(Fetot+Li) [=Fe#] formicas with VIR >2.5 a.p.f.u. and VIAl >0.5 a.p.f.u.; and VIAl/(VIAl+Fetot+Mg) [=Al#] formicas with VIR <2.5 a.p.f.u. The common true K micas plot predominantly within and between these series and have Mg6Li <0.3 a.p.f.u. Tainiolite is a mica with Mg6Li >0.7 a.p.f.u., or, fortr ansitional stages, 0.3–0.7 a.p.f.u. Some true K mica end-members, especially phlogopite, annite and muscovite, form binary solid solutions with non-K true micas and with brittle micas (6% of the micas studied). Graphical presentation of true K micas using the coordinates Mg minus Li (= mgli) and VIFetot+Mn+Ti minus VIAl (= feal) depends on theirclassification according to VIR and VIAl, complemented with the 50/50 rule.

Syntheses and Crystal Structures of the Bromide-derivatized Lanthanoid(III) Ortho-Oxomolybdates(VI) LnBr[MoO4] (Ln = Pr, Nd, Sm, Gd– Lu)

2013 ◽  
Vol 68 (5-6) ◽  
pp. 616-624 ◽  
Author(s):  
Tanja Schustereit ◽  
Harald Henning ◽  
Thomas Schleid ◽  
Ingo Hartenbach
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Coordination Number ◽  
Coordination Sphere ◽  
Space Group ◽  
Structural Arrangement ◽  
Common Structure ◽  
Coordination Spheres ◽  
The Common ◽  
Oxygen Atoms

The lanthanoid(III) bromide ortho-oxomolybdates(VI) LnBr[MoO4] (Ln = Pr, Nd, Sm, Gd - Lu) crystallize triclinically in the space group P1 (a=686 - 689, b=713 - 741, c=1066 - 1121 pm, a =103 - 106, b =107 - 108, g = 92 - 95°) with Z =4. The crystal structure contains two crystallographically distinguishable Ln3+ cations, each one with a coordination number of seven plus one. (Ln1)3+ is surrounded by three bromide and four plus one oxide anions, while for (Ln2)3+ just one bromide and six plus one oxide anions belong to the coordination sphere. Considering the smallest lanthanoids, however, the distances to the farthest anions increase so much that their contribution to the coordination spheres becomes negligible in both cases. The polyhedra around (Ln1)3+ are connected to each other via common edges, which consist of two crystallographically identical Br- anions (Br1). Furthermore, the common structure of the LnBr[MoO4] series contains two crystallographically different, discrete [MoO4]2- ortho-oxomolybdate(VI) tetrahedra. Two plus one oxygen atoms of each [(Mo1)O4]2- unit are used to interconnect the polyhedra around (Ln1)3+ and (Ln2)3+ together with one Br- anion (Br2). The connection between two polyhedra around (Ln2)3+ is generated exclusively by two plus one oxygen atoms of two [(Mo2)O4]2- anions. The complete structural arrangement can be considered as a bundle of primitively packed 1¥{LnBr[MoO4]} chains with two alternating motifs of linkage, which are running parallel along [012].

scholarly journals Crystal structures of bis[2-(diphenylphosphinothioyl)phenyl] ether and bis{2-[diphenyl(selanylidene)phosphanyl]phenyl} ether

2014 ◽  
Vol 70 (12) ◽  
pp. 536-540
Author(s):  
Daron E. Janzen ◽  
Arianna M. Kooyman ◽  
Kayla A. Lange
Keyword(s):  
Hydrogen Bonds ◽  
Crystal Structures ◽  
Phenyl Ether ◽  
Π Interactions ◽  
Twofold Axis ◽  
Phenyl Rings

The title compounds, C36H28OP2S2, (1), and C36H28OP2Se2, (2), exhibit remarkably similar structures although they are not isomorphous. The whole molecule of compound (2) is generated by twofold symmetry, with the ether O atom located on the twofold axis. Both compounds have intramolecular π–π interactions between terminal phenyl rings with centroid–centroid distances of 3.6214 (16) and 3.8027 (14) Å in (1) and (2), respectively. In the crystal of (1), short C—H...S hydrogen bonds link the molecules, forming chains along [001], while in (2) there are no analogous C—H...Se interactions present.

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